Intersection sizes of linear subspaces with the hypercube

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• Carla Groenland (University of Oxford)
• Thursday 07 November 2019, 14:30-15:30
• MR12.

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What are the possible intersection sizes that a k-dimensional subspace can have with the vertices of the n-dimensional hypercube (in Euclidean space)? Melo and Winter [arXiv:1712.01763, 2017] conjectured that all intersection sizes larger than 2 to the {k-1} (the “large” sizes) are of the form 2 to the {k-1} + 2 to the i. We show that this is almost true: the large intersection sizes are either of this form or of the form 35·2 to the {k-6} . We also disprove a second conjecture of Melo and Winter by proving that a positive fraction of the “small” values is missing. Joint work with Tom Johnson

This talk is part of the Combinatorics Seminar series.

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